Hudson Murder Suspect's Alibi Doesn't Add Up

Hudson Murder Suspect's Alibi

Doesn't Add Up

10/28/2008 5:30 AM PDT BY TMZ STAFF

The case is building quickly against William Balfour, the man police sources have pinpointed as the primary suspect in the murder of Jennifer Hudson's family.

More details are emerging: The Chicago Sun-Times is reporting Balfour's girlfriend -- whose house he was arrested at -- has contradicted Balfour's alibi and cops have caught him in at least one other lie. Police have been tracking him through cell phone records.

A neighbor says a man he believes to be Balfour was seen pulling up to his GF's house around noon on Friday, got out of the car "carrying what appeared to be a bottle of liquor," and was wearing a white hooded sweatshirt.

Balfour is in custody, and we're told he's considered the primary suspect.